DE 10 2007 047 671 A1 describes a powershift transmission for a motor vehicle, having a main transmission in the form of a dual-clutch transmission and a downstream transmission in the form of a planetary gearset that is connected downstream from the main transmission. The main transmission comprises a first partial transmission and a second partial transmission, wherein a first main transmission input shaft of the first partial transmission is associated with a first frictional powershift clutch and a separate, second main transmission input shaft of the second partial transmission is associated with a second frictional powershift clutch. Each of the two partial transmissions of the main transmission in the form of a dual-clutch transmission comprises, respectively, at least one interlocking shifting element. For the two partial transmissions a common main transmission output shaft is provided. The downstream transmission in the form of a planetary gearset comprises a downstream transmission input shaft and a downstream transmission output shaft. The output shaft of the main transmission can be coupled by means of an interlocking shifting element to a first planetary gearset element of the downstream transmission. A second planetary gearset element of the downstream transmission is connected fixed to the output shaft of the downstream transmission. A third planetary gearset element of the downstream transmission can be coupled by means of further interlocking shifting elements either to the transmission housing or to one of the other two planetary gearset elements.